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Conic Intersection Demo

Conic Intersection Demo
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2018-12-15 03:43
FunctionCoordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the intersection of cones. It involves core mathematical concepts such as cones, intersection, percentages, quadratic functions, definite integrals, slope, and arithmetic. The construction utilizes GeoGebra commands/objects like Intersect, Circle, Point, OrthogonalLine, Segment, Rotate, Angle, Ray, Locus, Mirror, and CircleArc. Suitable for high school and above, ideal for teaching solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, r1) → c
  3. Circle(A, d) → e
  4. Intersect(e, xAxis, 2) → B
  5. Circle(B, r2) → f
  6. Point(yAxis) → C
  7. OrthogonalLine(C, yAxis) → g
  8. Intersect(c, xAxis) → D, E
  9. Intersect(f, xAxis) → F, G
  10. OrthogonalLine(D, xAxis) → h
  11. OrthogonalLine(F, xAxis) → i
  12. OrthogonalLine(E, xAxis) → j
  13. OrthogonalLine(B, xAxis) → k
  14. OrthogonalLine(G, xAxis) → l
  15. Intersect(g, h) → H
  16. Intersect(g, i) → I
  17. Intersect(g, j) → J
  18. Intersect(g, k) → K
  19. Intersect(g, l) → L
  20. Circle(C, h1) → p
  21. Intersect(p, yAxis, 2) → M
  22. Circle(K, h2) → q
  23. Intersect(q, k, 2) → N
  24. Segment(M, H) → m
  25. Segment(M, J) → n
  26. Segment(N, I) → r
  27. Segment(N, L) → s
  28. Point(xAxis) → O
  29. Rotate(A, (-(45°)), O) → A'
  30. Angle(A', O, A) → α
  31. Ray(A', O) → t
  32. Point(t) → P
  33. Ray(P, O) → a
  34. Intersect(c, f) → Q, R, ,
  35. OrthogonalLine(Q, yAxis) → b
  36. OrthogonalLine(R, yAxis) → f_1
  37. Intersect(a, b) → S
  38. Intersect(f_1, a) → T
  39. OrthogonalLine(S, xAxis) → g_1
  40. OrthogonalLine(T, xAxis) → h_1
  41. Intersect(g, g_1) → U
  42. Intersect(g, h_1) → V
  43. Intersect(n, r) → W
  44. OrthogonalLine(W, g) → i_1
  45. Intersect(i_1, xAxis) → Z
  46. OrthogonalLine(W, yAxis) → j_1
  47. OrthogonalLine(O, xAxis) → k_1
  48. Intersect(j_1, k_1) → A_1
  49. Intersect(g, i_1) → B_1
  50. Segment(W, B_1) → l_1
  51. Point(l_1) → C_1
  52. OrthogonalLine(C_1, yAxis) → m_1
  53. Intersect(m_1, r) → D_1
  54. Intersect(m_1, n) → E_1
  55. OrthogonalLine(E_1, m_1) → n_1
  56. OrthogonalLine(D_1, m_1) → p_1
  57. Intersect(p_1, xAxis) → F_1
  58. Intersect(n_1, xAxis) → G_1
  59. Circle(A, G_1) → c_1
  60. Circle(B, F_1) → d_1
  61. Intersect(d_1, c_1) → H_1, I_1, ,
  62. OrthogonalLine(I_1, yAxis) → q_1
  63. OrthogonalLine(H_1, yAxis) → r_1
  64. Intersect(q_1, a) → J_1
  65. Intersect(r_1, a) → K_1
  66. OrthogonalLine(J_1, xAxis) → s_1
  67. OrthogonalLine(K_1, xAxis) → t_1
  68. Intersect(m_1, s_1) → L_1
  69. Intersect(m_1, t_1) → M_1
  70. Locus(L_1, C_1) → lieu1
  71. Locus(M_1, C_1) → lieu2
  72. OrthogonalLine(N_1, xAxis) → a_1
  73. Circle(N_1, a1) → e_1
  74. Intersect(e_1, a_1, 1) → O_1
  75. Rotate(O_1, α1, N_1) → P_1
  76. Angle(O_1, N_1, P_1) → β
  77. Mirror(P_1, a_1) → Q_1
  78. CircleArc(N_1, Q_1, P_1) → c_2
  79. Segment(N_1, P_1) → b_1
  80. Segment(N_1, Q_1) → f_2
  81. Locus(I_1, C_1) → lieu3
  82. Locus(H_1, C_1) → lieu4
  83. CircleArc(A, G_1, I_1) → arc
  84. Segment(M, E_1) → ai
  85. Circle(N_1, ai) → d_2
  86. Rotate(O_1, (360° * arc / ((π * ai))), N_1) → R_1
  87. Angle(O_1, N_1, R_1) → γ
  88. Segment(N_1, R_1) → g_2
  89. Intersect(d_2, g_2, 1) → S_1
  90. Locus(S_1, C_1) → lieu5
  91. Mirror(S_1, a_1) → T_1
  92. Locus(T_1, C_1) → lieu6